Question

A solution containing 29.75 {\rm {\rm mg}} of an unknown protein per 28.5 {\rm {\rm mL}} solution was found to have an osmotic pressure of 3.70 {\rm {\rm torr}} at 45 {\rm ^\circ {\rm C}} .

What is the molar mass of the protein?

Answer 1

Given,

Osmotic Pressure = 3.7 torr = 0.004868 atm

We know that,

Osmotic Pressure = CKT

where,

C = Molarity (mol/L)

K = Gas constant = 0.0821

T = Temperature = 45 degree C = 318 K

=> 0.004868 = C x 0.0821 x 318

=> C = 1.865 x 10^-4 M

Mass of Protien added = 29.75 mg = 0.02975 g

Volume of solution = 28.5 mL = 0.0285 L

Molarity = Moles / Volume

=> 1.865 x 10^-4 = Moles / 0.0285

=> Moles of Protien = 5.314 x 10^-6 moles

=> Molar Mass of Protien = 0.02975 / (5.314 x 10^-6) = 5598.4 g / mol